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The correlation coefficient is +1 in the case of a perfect direct (increasing) linear relationship (correlation), −1 in the case of a perfect inverse (decreasing) linear relationship (anti-correlation), [5] and some value in the open interval (,) in all other cases, indicating the degree of linear dependence between the variables. As it ...
If the predictor variables are correlated among themselves, the inverse of the correlation matrix accounts for this. The squared coefficient of multiple correlation can also be computed as the fraction of variance of the dependent variable that is explained by the independent variables, which in turn is 1 minus the unexplained fraction.
A correlation coefficient is a numerical measure of some type of linear correlation, meaning a statistical relationship between two variables. [ a ] The variables may be two columns of a given data set of observations, often called a sample , or two components of a multivariate random variable with a known distribution .
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
Intuitively, the Spearman correlation between two variables will be high when observations have a similar (or identical for a correlation of 1) rank (i.e. relative position label of the observations within the variable: 1st, 2nd, 3rd, etc.) between the two variables, and low when observations have a dissimilar (or fully opposed for a ...
There are many names for interaction information, including amount of information, [1] information correlation, [2] co-information, [3] and simply mutual information. [4] Interaction information expresses the amount of information (redundancy or synergy) bound up in a set of variables, beyond that which is present in any subset of those variables.
In statistics, canonical-correlation analysis (CCA), also called canonical variates analysis, is a way of inferring information from cross-covariance matrices.If we have two vectors X = (X 1, ..., X n) and Y = (Y 1, ..., Y m) of random variables, and there are correlations among the variables, then canonical-correlation analysis will find linear combinations of X and Y that have a maximum ...
Total correlation quantifies the amount of dependence among a group of variables. A near-zero total correlation indicates that the variables in the group are essentially statistically independent; they are completely unrelated, in the sense that knowing the value of one variable does not provide any clue as to the values of the other variables.